
to denote its material derivative.
In the bulk, we proceed exactly as in [1]} to reformulate (REF ) as
\(\begin{aligned}0 & \ge \textnormal {div}\big [J_e- \tfrac{1}{2} \left| {v} \right|^2 J+ \top {v}- \mu J_\phi + \partial _{\nabla \phi }f D_t \phi \big ]\\& \quad + \big [ \partial _{\phi }f- \textnormal {div}(\partial _{\nabla \phi }f)- \mu \big ]D_t \phi \\& \quad - \big [  \nabla \phi \otimes \partial _{\nabla \phi }f\big ] : \nabla {v}+ \nabla \mu \cdot J_\phi &&\quad \text{in $Q$.}\end{aligned}\) 
